No log for adding email to a customer
By default, for every activity performed on the Chargebee site, there will be an activity log created. If the email details are given during customer creation then the event when the email got added is not logged separately. It just shows as a 'Customer created' event.
There are two instances where the email address of the customer gets recorded in Chargebee.
While creating a customer if the email address was added along with the other details then you will find the Activity log as ‘Customer created’. You can click on three ellipses to have a detailed view.
The detailed view will have the email address
If the email address is updated individually, then you will have a unique event created.
You can find the ‘Activity log’ section at the bottom of the Customer section and it applies to every other setting as well.